Aboat travels upstream for 120 miles in 3 hours and returns in 2 hours traveling downstream in a local stream of water. what is the rate of the boat in still water and the rate of the current?

Let the rate of the current be x mph and rate of the boat in still water be y mph.

So the relative speed of the boat with the current ( downstream) = y + x and against the current (upstream) it = y - x.

Then , using speed = distance / time:-

y - x = 120/3 = 40

y + x = 120/2 = 60

Adding the 2 equations:-

2y = 100

y = 50

And substituting in the frst equation:-

50 - x = 40

x = 10

- Rate of boat in still water = 50 mph and rate of the current = 10 mph.

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